The only spells I can find with this feature:
Spell |
Level |
Source |
Chill touch |
- Cold, death master, dread necromancer, duskblade, sha’ir, sorcerer, Telflammar shadowlord, warmage, wizard
- Blighter
|
Player’s Handbook |
Corrosive grasp |
- Sorcerer, wizard
|
Spell Compendium |
Handfire |
- Cleric, druid, Harper scout, hathran, ranger
(each of Selûne)
|
Magic of Faerûn |
Handfire |
- Initiate of Selûne
|
Player’s Guide to Faerûn |
Parching touch |
- Sorcerer, thirst, wizard
|
Sandstorm |
Storm touch |
- Sorcerer, wizard
|
Magic of Eberron |
Scalding touch |
- Sorcerer, wizard
|
Magic of Eberron |
Touch of the grave |
- Sorcerer, wizard
|
Complete Mage |
Handfire
You’ll note that handfire is the only one available as a cleric spell, whether the Magic of Faerûn version that is just a cleric spell (but only for clerics of Selûne), or the Player’s Guide to Faerûn version that requires the Initiate of Selûne feat (which requires being a cleric, druid, hathran, or ranger of Selûne).
Note that Eberron Campaign Setting claims, as the first of the “Ten Things You Need to Know” on page 8, that “If it exists in D&D, then it has a place in Eberron,” (emphasis original). As handfire exists in D&D, it therefore has a place in Eberron. Where that place is, of course, is left undefined and up to your DM, but you can ask your DM about how it might be accessed—maybe it’s a cleric spell, maybe just for certain clerics, as in the Magic of Faerûn version, or maybe, like Player’s Guide to Faerûn, you need to take some Initiate feat. Eberron doesn’t have any distinctly moon-themed deities, but of course the moons are a very big deal in Eberron, and totally plausible as a focus of worship—after all, many druids and rangers in the Eldeen Reaches do. Handfire itself would also be exceptionally fitting for the Church of the Silver Flame, as would most of the rest of the Initiate of Selûne spells if you file off the moon theming (e.g. argent blade, wall of silver, argent path, argent shield)—aside from strength of the beast, which would need to be replaced as that one doesn’t fit the Silver Flame at all.
Domain spells
As you note in your question, chill touch and parching touch are on the cold and thirst domains, respectively. As Maxime Cuillerier’s fine answer points out, Player’s Handbook II has a spontaneous domain spells option for clerics to make those far more accessible. There are also other, similar, though weaker, options:
The Domain Spontaneity feat from Complete Divine, burn a use of turn/rebuke undead to swap a spell for a domain spell of the spell’s level or lower.
A 10,000-gp domain icon wondrous item from Faiths of Eberron, 3/day swap a spell for a domain spell of the spell’s level or lower. Doesn’t actually require that you have the domain in question, just that you worship a faith that offers it. Could get multiple for more uses per day, or arguably, per the magic item creation guidelines, could get a custom one with unlimited uses per day for 16,667 gp.
A 36,000-gp domain staff from Complete Champion, 1/day per spell level swap a spell for a domain spell of that level. Overpriced and not recommended.
Other options
Complete Mage allows a cleric to be a divine magician: sacrifice a domain in order to pick one abjuration, divination, or necromancy wizard spell per spell level to add to your cleric list. That could let you get either chill touch or parching touch (parching touch is much better, as desiccation damage carries an automatic fatigue rider), as well as touch of the grave much later on (corrosive grasp is a conjuration, storm touch and scaling touch are evocations).
There’s also the Extra Spell feat, from Complete Arcane. Nothing in the feat says you have to choose a spell from a spell list you actually have access to. Few DMs actually allow you to do that, though, either because they feel that’s imbalanced and just don’t allow it (which is fair, though I am not sure I agree), or because they’re convinced that the feat actually bars it somehow (the arguments for this are convoluted, and I personally find them unconvincing, but nonetheless they exist).
Conclusion
Since the cold and thirst domains are pretty meh, divine magician may be better than spontaneous domain spells. Any of the other options are far pricier, requiring a feat or expensive magic items, unless your DM lets you just have handfire as clerics of Selûne could under Magic of Faerûn rules.